Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic-to-nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau-de Gennes model for rod-like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic-isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic-nematic interface and the substrate-nematic-isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Orientational ordering in the nematic phase of 4-alkenyl-substituted bicyclohexylnitriles

The orientational ordering of a series of 4-alkenyl-substituted bicyclohexyl liquid crystals was studied by natural abundance ¹³C NMR spectroscopy. A combination of the methods of variable angle spinning (VAS) and separated local field spectroscopy (SLF) was used. Rapid sample spinning about an axis forming an angle of about 65° with respect to the magnetic field forces the nematic director to align parallel to the spinnin axis, leading to narrow peaks in the ¹³C NMR spectrum. The two-dimensional NMR spectroscopic method SLF allows the observation of decoupled ¹³C signals in the ω₂ dimension and first-order C-H splitting patterns in the ω₁ dimension, from which the C-H dipolar coupling constants for individual pairs of nuclei can be obtained. Then, the order parameters for different molecular segments can be calculated. The method was applied to five different 4-alkenyl-substituted cyanobicyclohexanes. For the compounds studied, the dependence of the ring order parameters on the alkenyl chains shows the same trend as the melting and clearing temperatures and the elastic constants.     

Orientational ordering in the nematic phase of 4-alkyl-4'-cyanobicyclohexanes

The orientational ordering of three liquid crystals (trans,trans-4-n-alkyl-4'-cyanobicyclohexanes) has been investigated using ¹³C NMR. 2D proton-encoded local field spectroscopy was used to determine the ¹³C-¹H dipolar coupling constants, from which the order parameters were calculated. Semi-empirical linear relations between the obtained order parameters and anisotropic ¹³C chemical shifts were established. It was found that the order parameters of the major axis of the cyclohexane rings are smaller than those of liquid crystals with phenyl rings, and the order parameters of the C-H bonds in the aliphatic chains also behave differently.     

Orientational ordering in the nematic phase of 4-alkyl-4'-cyanobicyclohexanes

The orientational ordering of three liquid crystals (trans,trans-4-n-alkyl-4'-cyanobicyclohexanes) has been investigated using ¹³C NMR. 2D proton-encoded local field spectroscopy was used to determine the ¹³C-¹H dipolar coupling constants, from which the order parameters were calculated. Semi-empirical linear relations between the obtained order parameters and anisotropic ¹³C chemical shifts were established. It was found that the order parameters of the major axis of the cyclohexane rings are smaller than those of liquid crystals with phenyl rings, and the order parameters of the C-H bonds in the aliphatic chains also behave differently.     

Mechanical model for filament buckling and growth by phase ordering

A mechanical model of open filament shape and growth driven by phase ordering is formulated. For a given phase-ordering driving force, the model output is the filament shape evolution and the filament end-point kinematics. The linearized model for the slope of the filament is the Cahn-Hilliard model of spinodal decomposition, where the buckling corresponds to concentration fluctuations. Two modes are predicted: (i) sequential growth and buckling and (ii) simultaneous buckling and growth. The relation among the maximum buckling rate, filament tension, and matrix viscosity is given. These results contribute to ongoing work in smectic A filament buckling.     

Carbon film growth on iron substrates by a CVD method

Carbon film coatings have been produced by a hot‐wall chemical vapor deposition (CVD) method under moderate conditions from pyrolysis of a mixture of propane and argon on an Fe(110) substrate at temperatures of 800–900 °C for different deposition times. The effects of temperature and reaction time on the growth of the carbon films were studied. Field‐emission scanning electron microscopy (FESEM), Raman microscopy, Auger electron spectroscopy (AES) and x‐ray diffraction methods have been performed to study the surface morphologies, growth features and microstructures of the carbon film coatings. The FESEM analyses indicated that carbon films on an Fe substrate consisted of flat‐layer and filamentous morphologies. Raman and AES analyses showed that the carbon initially was crystalline but the degree of disorder in the top layer of the carbon film increased with increasing deposition temperature. High‐resolution transmission electron microscopy studies are also in agreement with Raman results. The same trend was observed when the deposition time was increased from 5 to 30 min. Copyright © 2005 John Wiley & Sons, Ltd.     

Tricritical point induced by smectic ordering of a nematic gel

The authors study volume phase transitions of a nematic gel immersed in a liquid crystal (LC) solvent, which shows a second-order nematic-smectic A phase transition (NST). Combining Flory's elastic energy [Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953)] for a swelling of the gel with the McMillan model [Phys. Rev. A 4, 1238 (1971)] for smectic ordering, the authors calculate the equilibrium swelling of the gel and smectic order parameters as a function of temperature. The authors take into account an attractive interaction parameter c between the gel and LC solvents. On increasing the value of the coupling constant c, a second-order NST of the gel is changed to a first-order one and a continuous volume phase transition of the gel is changed to a discontinuous one. The authors find a tricritical point of the gel induced by smectic ordering.     

Theory of an electric field induced periodic phase in a nematic film

The elastic theory of nemtatic liquid crystals is used to determine whether it gives support for recent experimental observations of a novel periodic phase occurring in homeotropically aligned films when an electric field is applied in the plane of the film. The director remains in the plane defined by the film normal and the field, and the wavevector of the periodicity is parallel to the field. It is found that the theory is consistent with experiment.     

Phase ordering of the liquid crystalline 'B7' phase by analysis of fractal growth patterns

The phase ordering process of bent-core mesogenic molecules is qualitatively different from that observed for conventional rod-like (calamitic) mesogens. Fractal dimensional analysis can be employed to characterize the phase ordering process of these unconventional mesogens. The phase transition between the isotropic melt and the liquid crystalline 'B₇' phase of a 'banana-molecule' material has been investigated in terms of fractal growth patterns, with respect to sample thickness and rate of temperature change. It is shown, that there is a crossover from confinement dominated phase growth to volume behaviour, while the cooling rate has no influence on the dimension of the fractal patterns observed during the phase ordering process.     

Phase ordering of the liquid crystalline 'B7' phase by analysis of fractal growth patterns

The phase ordering process of bent-core mesogenic molecules is qualitatively different from that observed for conventional rod-like (calamitic) mesogens. Fractal dimensional analysis can be employed to characterize the phase ordering process of these unconventional mesogens. The phase transition between the isotropic melt and the liquid crystalline 'B₇' phase of a 'banana-molecule' material has been investigated in terms of fractal growth patterns, with respect to sample thickness and rate of temperature change. It is shown, that there is a crossover from confinement dominated phase growth to volume behaviour, while the cooling rate has no influence on the dimension of the fractal patterns observed during the phase ordering process.     

Unexpected high ordering of a [60]Fullerene nitroxide in the nematic phase of 4-4'-azoxyanisole

A nitroxide [60]fullerene adduct containing a pyrrolidine-1-oxyl group has been synthesized. Its orientational order in the nematic phase of the liquid crystal solvent 4,4'-azoxyanisole (PAA) has been measured from the variation of the EPR spectral parameters on passing from the isotropic to the nematic phase. Highly resolved EPR lines allow for precise evaluation of the shifts of the g , a N and a H values. Since the g and the hyperfine tensors are known, the order matrix could be obtained. This is compared with the one calculated with a theoretical model based on short range solute-solvent interactions, which predicts a considerable degree of orientation of the molecular axes, despite the almost spherical shape of the molecule. The agreement with experimental findings is quite good and it is further improved if a bent structure of the pyrrolidine ring is taken into account.     

Dynamic simulation of droplet interaction and self-assembly in a nematic liquid crystal

We use dynamic simulations to explore the pairwise interaction and multiparticle assembly of droplets suspended in a nematic liquid crystal. The computation is based on a regularized Leslie-Ericksen theory that allows orientational defects. The homeotropic anchoring on the drop surface is of sufficient strength as to produce a satellite point defect near the droplet. Based on the position of the defects relative to the host droplet and the far-field molecular orientation, we have identified five types of pairwise attractive and repulsive forces. In particular, long-range attraction between two droplets with their line of centers along the far-field orientation decays as R-4, with R being the center-to-center separation. This agrees with prior static calculations and a phenomenological model that treats the attraction as that between two dipoles. For interaction in shorter ranges, our simulations agree qualitatively with experimental measurements and static calculations. However, there is considerable quantitative discrepancy among the few existing studies and our simulation. We suggest that this is partly due to the dynamic nature of the process, which has never been taken into account in prior calculations. Multidrop simulations show the formation of linear chains through pairwise interactions between nearby droplets. Parallel chains repel or attract each other depending on the relative orientation of the drop-to-defect vector. These are consistent with experimental observations of chain formation and two-dimensional self-assembly in bulk nematics and smectic-C films.     

Molecular structure of pyrimidine by NMR in the nematic phase

The NMR spectrum of pyrimidine has been studied in the nematic phase of 4-methoxy benzylidene-4-amino-α-methyl cinnamic acid-n-propyl ester at room temperature. The ratios of all the interproton distances are determined and found to differ significantly from those obtained from microwave data. The molecule, like other aromatics, is shown to orient preferentially with its plane in the direction of the magnetic field.     

End-chain ordering and even-odd effects in nematic thermotropic liquid crystalline mesophases studied by deuterium magnetic resonance

Deuterium quadrupole splittings are reported for the nematic mesophases of all isomers of 4,4′-di-n-octyl-d₄(d₆)-oxyazoxybenzene with CD₂(CD₃) groups at corresponding segments in the two end chains. These splittings do not decrease monotonically with increasing separation of the chain segment from the aromatic core as has previously been assumed. Comparison with similar measurements for 4,4′-di-n-heptyloxyazoxybenzene reveals an “even—odd” effect in the chain ordering, but only in so far as to reflect differences in the molecular order in the two mesophases. The results are used to test earlier theoretical calculations by Mar?elja.     

Directed polystyrene/poly(methyl methacrylate) phase separation and nanoparticle ordering on transparent chemically patterned substrates

We investigate the surface-directed phase separation of spin-coated polystyrene/poly(methyl methacrylate) (PS/PMMA) blends on prepatterned octadecyltrichlorosilane (OTS)-glass substrates under various experimental conditions. As a result of tandem processes of spinodal decomposition and selective wetting of polymer components during spin-coating, low-energy OTS stripes and high-energy glass surfaces laterally arrange the phase-separated polymers according to the chemical pattern on the substrate. Optimal pattern replication was achieved when the length scale of phase separation, controlled via the polymer concentration of the spin-coating solution, matched the smallest feature dimension in a striped chemical pattern possessing two alternating distances between stripes. It was also shown that polymer blend patterns were most closely registered with the underlying substrate when the PS/PMMA composition ratio (30/70, w/w) matched the areal fraction of OTS on the glass surface (～30%). The influence of solvents demonstrated that a solvent with a relatively low volatility, such toluene, was required for patterning so that domain feature sizes were able to coarsen to the size of the patterned features before film vitrification. As well, we showed that the technique and optimized conditions developed in this study could be applied to pattern photoluminescent CdS quantum dots into microscale arrays of parallel lines via spin-coating onto transparent OTS-glass substrates.     

Dispersion control and nematic ordering of Ni/Al layered double hydroxide suspensions

In this paper, we report the preparation of aqueous suspensions of Ni/Al layered double hydroxide (LDH) nanoparticles by a non-steady co-precipitation followed by peptization. By choosing suitable peptization temperature and time, well-dispersed suspensions were obtained. Meanwhile, the particle size, shape and size polydispersity can be efficiently controlled. Nematic ordering is observed in colloidal Ni/Al LDH suspensions and confirmed by birefringence observations and SAXS measurements. Furthermore, we showed that the sol-gel transition takes place after a liquid crystalline phase transition in concentrated Ni/Al LDH suspensions. The absence of isotropic-nematic phase separation can be attributed to the fact that the nematic phase droplets are too small to settle to the bottom of the cuvette.     

Effect of nematic ordering on the elasticity and yielding in disordered polymeric solids

The relation between elasticity and yielding is investigated in a model polymer solid by Molecular‐Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers — both with bond disorder — as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio τ_Y/G between the shear yield strength τ_Y and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the shear modulus and the decrease of the shear yield strength, as observed in experiments on nematic thermosets. A tentative explanation of the subsequent reduction of the ratio τ_Y/G in terms of the distributions of the per‐monomer stress is offered. © 2017 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2017 , 55, 1760–1769     

Computational modelling of radiative Maxwell fluid flow over a stretching sheet containing nanoparticles with chemical reaction

In the presence of thermal radiation, heat generation/absorption, and chemical reaction, the heat and mass transmission characteristics of a 2-D electrically conducting incompressible Maxwell fluid past a stretched sheet have been examined. There are various real-world applications for this issue, notably the extrusion of polymers and metal thinning. The transport equations take into account Brownian motion as well as thermophoresis when there is a chemical reaction involved. By making use of the relevant similarity variables, the PDEs that govern the stream and the boundary conditions that go along with them may be non-dimensionalized. The ensuing transformed ODEs are solved using the fourth- and fifth-order Runge-Kutta-Fehlberg scheme. It has been determined and quantitatively examined how the different embedded thermo-physical factors influence the velocity, temperature, and concentration. A case study comparison between our findings and those published in the literature reveals a high degree of agreement. Raising the value of the chemical reaction parameter causes a narrowing of the concentration distribution while increasing the temperature causes thermal radiation to have a greater impact. As the quantity of Nt increases, the thickness of the boundary layer grows, causing the surface temperature to increase, ensuing in a temperature increase.     

Dendrite-like texture growth in the nematic liquid crystal phase of 4-n-heptyl- and 4-n-octyl-oxybenzoic acids aligned by a polyimide coating

An oriented dendrite-like texture is reported, appearing at a definite temperature in the nematic phase range of 4-n-heptyl- and 4-n-octyl-oxybenzoic acids (HOBA and OOBA), aligned by rubbed polyimide and preceding the smectic C phase, on cooling. Two preferred directions with respect to the 'easy' axis are indicated in the dendrites grown of HOBA and OOBA. We discuss a possible mechanism, at molecular and supramolecular levels, for this dendrite growth; and assume that the building 'blocks' of the dendrites are oligomers, or mixture of oligomers with 'free' closed and open dimers, constituting a detached crystalline layered state (named by us SmX, a smectic state intermediate between the N₁ ordinary nematic and SmC phases). The study of the dynamics of the dendrite growth demonstrates a scaling relationship typical for non-equilibrium systems. The observed dendrites can be considered as patterns formed in complex non-linear dissipative systems, driven outside of equilibrium.     

Dendrite-like texture growth in the nematic liquid crystal phase of 4-n-heptyl- and 4-n-octyl-oxybenzoic acids aligned by a polyimide coating

An oriented dendrite-like texture is reported, appearing at a definite temperature in the nematic phase range of 4-n-heptyl- and 4-n-octyl-oxybenzoic acids (HOBA and OOBA), aligned by rubbed polyimide and preceding the smectic C phase, on cooling. Two preferred directions with respect to the ‘easy’ axis are indicated in the dendrites grown of HOBA and OOBA. We discuss a possible mechanism, at molecular and supramolecular levels, for this dendrite growth; and assume that the building ‘blocks' of the dendrites are oligomers, or mixture of oligomers with ‘free’ closed and open dimers, constituting a detached crystalline layered state (named by us SmX, a smectic state intermediate between the N₁ ordinary nematic and SmC phases). The study of the dynamics of the dendrite growth demonstrates a scaling relationship typical for non-equilibrium systems. The observed dendrites can be considered as patterns formed in complex non-linear dissipative systems, driven outside of equilibrium.